Question 1
Evaluate $\int (3e^x + 2) \, dx$.
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Mathematical Methods Β· Unit 3 Β· Introduction to integration Β· Anti-differentiation
Use the formula β« ππ₯ ππ₯ = ππ₯ + π.
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Question 2
Determine β«(2e^x + 7) dx
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Question 3
A function N(t) satisfies the differential equation dN/dt = -3e^t, where t is measured in hours. (a) Find the general solution N(t) by integrating. (1 mark) (b) Given that N(0) = 2500, determine the particular solution for N(t). (2 marks)
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Question 4
A pharmaceutical company models the concentration of a drug in a patient's bloodstream (in mg/L) by the rate function $\frac{dC}{dt} = 8e^t$, where $t$ is the time in hours after administration. The concentration at $t = 0$ is $C(0) = 2$ mg/L. Use this information to find the concentration at $t = 2$ hours, correct to 2 decimal places.
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